Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 1274

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\[1)\ ctg\left( \text{arctg\ }\sqrt{3} \right) =\]

\[= \frac{1}{\text{tg}\left( \text{arctg\ }\sqrt{3} \right)} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3};\]

\[2)\ ctg(arctg\ 1) =\]

\[= \frac{1}{\text{tg}(arctg\ 1)} = \frac{1}{1} = 1;\]

\[3)\sin\left( \text{arctg}\left( - \sqrt{3} \right) \right) =\]

\[= \sin\left( - arctg\ \sqrt{3} \right) =\]

\[= - \sin\frac{\pi}{3} = - \frac{\sqrt{3}}{2};\]

\[4)\sin\left( \text{arctg}\frac{1}{\sqrt{3}} \right) = \sin\frac{\pi}{6} = \frac{1}{2};\]

\[5)\cos(arctg\ 1) = \cos\frac{\pi}{4} = \frac{\sqrt{2}}{2};\]

\[6)\cos\left( \text{arctg}\left( - \sqrt{3} \right) \right) =\]

\[= \cos\left( - arctg\ \sqrt{3} \right) = \cos\frac{\pi}{3} = \frac{1}{2}.\]